Extending the analytic approximation for calculating momentum enhancement in hazardous object mitigation scenarios with a variable ejecta velocity.

Abstract:

Momentum enhancement, β, has emerged as a figure of merit in work done as part of the NASA and NNSA inter-agency collaboration studying the possibility of preventing as asteroid or comet from impacting the Earth (Dearborn et al., 2020). Beta is the ratio of the change of momentum of the remaining asteroid to that of the impactor (Holsapple & Housen, 2012). Work presented in Takada and Kurosawa, 2019, which built on established analytic impact approaches (Holsapple, 1983; Melosh, 1984), provided a path to an analytic treatment of 𝛽 which accounts for the different ejection velocities experienced by the ejecta lofted from different areas within the crater. The updated analytic solution for momentum enhancement parameters provides a more careful treatment of crater ejecta and its contribution to momentum enhancement and resulting velocity change of the target object. Table 1 compares results from the updated analytic treatment and the prior method to that captured numerically using the Lagrangian hydrocode FLAG (Plesko et al., 2019). The updated momentum enhancement values are in better agreement with numerical simulations than the prior method, but may not account for all contributions of momentum enhancement. This approach provides a quick tool for sensitivity analysis of variables related to deflection scenarios, which may inform more intensive numerical studies.

Table 1: Characteristics of target and projectile within each case study along with original analytic approximations for 𝛽 and Δ𝑣, the numerical results for both, and updated analytic approximations (𝛽𝑛ew). The final rows show 𝛽 values for each case study at the upper and lower bounds of yield strength.